Why was the Virginia Plan introduced and amended and the New Jersey Plan introduced and rejected?

1. The rate at which people enter a movie theater on a given day is modeled by the function S defined by S(t) = 80 -12 cos 6 The

Arlecino [84]

Hi there!

a.

To find the total amount of people that have ENTERED by t = 20, we must take the integral of the appropriate function.

$\text{Amount that entered} = \int\limits^{20}_{10} {S(t)} \, dt \\\\ = \int\limits^{20}_{10} {80 - 12cos(\frac{t}{5})} \, dt$

Evaluate using a calculator:

$= 899.97 \approx \boxed{900\text{ people}}$

b.

To solve, we can find the total amount of people that have entered of the interval and subtract the total amount of people that have left from this value.

In other terms:
$\text{Amount of people} = \int\limits^{20}_{10} {S(t)} \, dt - \int\limits^{20}_{10} {R(t)} \, dt$

We can evaluate using a calculator (math-9 on T1-84):

$\text{\# of people} = \int\limits^{20}_{10} {80-12cos(\frac{t}{5})} \, dt - \int\limits^{20}_{10} {12e^{\frac{t}{10}}+20} \, dt$

$= 899.97 - 760.49 = 139.47 \approx \boxed{139 \text{ people}}$

c.

If:
$P(t) = \int\limits^t_{10} {S(t) - R(t)} \, dt$

Then:

$\frac{dP}{dt} = P'(t)= \frac{d}{dt}\int\limits^t_{10} {S(t) - R(t)} \, dt = S(t) - R(t)$

Evaluate at t = 20:

$S(20) = 80 - 12cos(\frac{20}{5}) = 87.844\\\\R(20) = 12e^{\frac{20}{10}} + 20 = 108.669$

$S(20) - R(20) = 87.844 - 108.669 = -20.823$

This means that at t = 20, there is a NET DECREASE of people at the movie theater of around 20.823 (21) people per hour.

d.

To find the maximum, we must use the first-derivative test.

Set S(t) - R(t) equal to 0:

$80 - 12cos(\frac{t}{5}) - 12e^{\frac{t}{10}} - 20 = 0\\\\60 - 12(cos(\frac{t}{5}) + e^{\frac{t}{10}})= 0$

Graph the function with a graphing calculator and set the function equal to y = 0:

According to the graph, the graph of the first derivative changes from POSITIVE to NEGATIVE at t ≈ 17.78 hours, so there is a MAXIMUM at this value.

Thus, at t = 17.78 hours, the amount of people at the movie theater is a MAXIMUM.

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At the community scale, how does a farmers market demonstrate the principles of fair trade?

vovangra [49]

Explanation:

A product must be produced by a farmer, cooperative, or worker that meet certain standard set by the fair trade labeling body

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What is one power of the government that is exclusively a power of the states?

Tamiku [17]

Answer:

government have the power to tax, make and enforce laws, charter banks, and borrow money.

Explanation:

If you need an explanation for each brack well

The legislative branch drafts proposed laws, confirms or rejects presidential nominations for heads of federal agencies, federal judges, and the Supreme Court, and has the authority to declare war.

The executive branch carries out and enforces laws. It includes the president, vice president, the Cabinet, executive departments, independent agencies, and other boards, commissions, and committees.

The judicial branch of the U.S. government is the system of federal courts and judges that interprets laws made by the legislative branch and enforced by the executive branch. At the top of the judicial branch are the nine justices of the Supreme Court, the highest court in the United States.

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The pitcher for the home team allows a lead-off double in the bottom half of the first inning of a Little League (Major) Division softball game. After returning to the pitcher's circle, the pitcher begins her wind-up to the next batter.

Explanation:

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being able to read and write, they would ask blacks a really hard question on theology or something about the constitution and then ask the next guy in line to write the letter

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